class Solution {
    public:
        int minInsertions(string s) {
            int n = s.size();
            vector<vector<int>> dp(n,vector<int>(n));
            for(int i = n-1 ; i >=0 ; i--){
                for(int j= i ; j < n ; j++){
                    if(s[i] == s[j]){
                        dp[i][j] = i+1 < j ? dp[i+1][j-1] : 0;
                    }else{
                        dp[i][j] = min({dp[i+1][j-1]+2,dp[i][j-1]+1,dp[i+1][j]+1});
                    }
                }
            }
            return dp[0][n-1];
        }
    };